# Deterministic Chaos

## 6.J. Bifurcation Diagrams for the

## Tent Map and the Logistic Map

For the logistic map the range of s-values is
0 <= s <= 4. Here is a picture of the diagram.

The logistic bifurcation diagram certainly has much more structure
than the tent bifurcation diagram. One thing we notice is the big sequence of branches
(starting at s = 3) opening to the right. This is the sequence of period-doubling
bifurcations,

where the non-zero fixed point gives rise to a 2-cycle,

that gives rise to a 4-cycle,

that gives rise to an 8-cycle, and so on.

Moreover, at least one of the
periodic windows seems to be visible around s = 3.85. We investigate this window
with a zoom.

Return to Bifurcation Diagrams for the
Tent Map and the Logistic Map.